Gram-Schmidt forward-backward generalized sidelobe canceller

Addressed here is the the discrete-time and the continuous-time recursive least-squares (RLS) modified Gram-Schmidt orthogonalization (MGSO) algorithms for forward-backward (FB) generalized sidelobe cancelling (GSC) adaptive beamformers. The FB-GSC requires processing each input data twice, forward and conjugated backward, and hence its adaptation would require a rank-two update each time. This paper first derives a discrete-time rank-two-update RLS MGSO algorithm for this purpose. Then, by imposing the conjugate symmetry constraints, the backward data processing can be removed without any loss and the complex-valued algorithm can be further transformed into an equivalent real-valued algorithm Therefore, significant computation savings can be achieved. Also described here is the continuous-time RLS MGSO algorithms for the FB-GSC and the conjugate symmetric FB-GSC. Computer simulations of the FB-GSC and the forward-only GSC are presented